1. Introduction to Workshop 10 Choosing Learning and Teaching Approaches and Strategies

2. Guiding Principles for Workshop 10: a rationale for the effective learning and teaching of mathematics Knowledge: can be procedural and conceptual Learning: the process and the learning outcomes in the syllabus – strong procedural skills and problem solving are of equal importance. Setting clear learning targets is essential for teachers and students. Teaching for Understanding: enabling students to think flexibly and inquire critically.

3. Guiding Principles for Workshop 10: A rationale for the effective learning and teaching of mathematics Prior knowledge A wide range of pedagogies: many strategies complement each other. Quality interaction: effective questioning and feedback guide the learning process. Teaching for independent learning: this should be nurtured. Feedback and assessment: not confined to giving a grade, but a wide range of strengths and weaknesses where learning can be improved. Resources: make use of a wide variety

4. Engagement of students: they participate actively, collaborate closely, express themselves openly, treat suggestions positively. Learner Diversity Literacy and Numeracy Guiding Principles for Workshop 10: A rationale for the effective learning and teaching of mathematics

5. Effective delivery of the syllabus: Common Pedagogical Approaches: 1. using an understanding of basic rules and skills approach 2. using an enquiry approach 3. using a co-construction approach 4. using a problem- solving approach. A single approach is rarely adopted, effective teachers integrate various strategies when teaching a topic

6. Workshop 10 Choosing Learning and Teaching Approaches and Strategies Session A: 9.30 – 10.15 Introduction & Lesson Study as a form of professional development Session B: 10.15 – 11.00 Cultivating skills for problem solving Tea & Coffee 11.00 – 11.15 Session C: 11.15 – 1.00 Teaching as co-construction 1.00-2.00 Lunch Session D : 2.00 – 2.45 Teaching as enquiry Session D: 2.45 – 3.30 Problem-solving learning

7. Summary Workshops 1-10 have highlighted the underlying principles of an effective mathematics classroom that is applicable to all levels at Junior and Senior Cycle. have set the direction for the teaching, learning and assessment (formative) of mathematics. have emphasised mathematical problem solving as being central to the learning of mathematics, involving A. the acquisition and application of mathematics concepts and skills in a wide range of situations, including closed, open-ended and real-world problems B. the development of mathematical problem- solving ability, which is dependent on five inter- related components – 1.Concepts, 2.Skills, 3.Processes, 5.Attitudes and 5.Metacognition

8. 1. Concepts Mathematical Concepts cover numerical, algebraic, geometrical, statistical, probabilistic and analytical concepts. Students should develop and explore mathematical ideas in depth and see that mathematics is an integrated whole, not merely isolated pieces of knowledge. Students should be given a variety of learning experiences to help them develop a deep understanding of concepts, to make sense of ideas as well as their connections and applications. Use of concrete materials, practical work and ICT should be part of the learning experience.

9. 2. Skills Includes procedural skills for numerical calculation, algebraic manipulation, spatial visualisation, data analysis, measurement, use of mathematical tools, technology and estimation. Development of skill proficiencies in students is essential in the learning and application of mathematics. Students should become competent in the various skills; over-emphasising skills without understanding the underlying principles should be avoided. It is also important to incorporate the use of thinking skills in the process of the development of skill proficiencies.

10. 3. Processes ‘Mathematical Processes’ refers to the knowledge skills involved in acquiring and applying mathematics. It includes reasoning, communication (using mathematical language to express ideas precisely, concisely and logically) and connections (seeing and making linkages among mathematical ideas, between maths and other subjects and between maths and everyday life), thinking skills and heuristics (giving a representation, looking for patterns, working backwards, solving a problem), application and modelling.

11. 4. Attitudes Affective aspects of maths learning: beliefs about maths and its usefulness interest and enjoyment in learning maths appreciation of the beauty and power of maths confidence in using maths perseverance in solving a problem. These are shaped by their learning experiences.

12. 5. Metacognition In particular, the selection and use of problem-solving strategies Experience is necessary to develop students’ problem-solving abilities Activities used to enrich metacognitive experience Expose students to general problem-solving skills and how these skills can be used to solve problems. Encourage students to think aloud about the strategies and methods they use to solve problems. Provide students with problems that require planning (before solving) and evaluation (after solving). Encourage students to seek alternative ways of solving the same problem and check the reasonableness of their answer. Allow students to discuss how to solve a particular problem and to explain the different methods that they use for solving a problem.